Hydro-Thermal-Wind Integrated Optimal Generation ...

Hydro-Thermal-Wind Integrated Optimal Generation Scheduling

of GENCOs in a Competitive joint Energy and Reserve Market

T.Anbazhagi, K. Asokan and R. Ashokkumar

Research Scholar, Department of Electrical Engineering, Annamalai University, Annamalai nagar, Tamil nadu, India.

Assistant professor, Department of Electrical Engineering, Annamalai University, Annamalai nagar, Tamil nadu, India

Professor, Department of Electrical Engineering, Annamalai University, Annamalai nagar, Tamil nadu, India

[email protected], [email protected] , [email protected]

Abstract:-

This paper solves the generation scheduling problem in a joint energy and reserve

competitive electricity market considering renewable energy sources of hydro and wind

generating units. A computational intelligent approach of an Improved Ant line optimizer

(IALO) is proposed to solve the problem. The prime objective of problem is to maximize the

profit of GENCOs and satisfying the standard system, thermal, hydro and wind plants

constraints. Here, schedule the generators with and without reserve power generation in a

joint energy and reserve market for improve the profit of GENCOs. The projected ALO

algorithm is based on the best and worst solutions obtained during the optimization process

and the random interactions between the candidate solutions. It require only the common

control parameters like population size and number of iterations and do not require any

algorithm-specific control parameters. In the proposed algorithm, the search space is

explored by the ant lion optimization first, and then the domain is searched by the particle

swarm optimization (PSO) in each iteration cycle. Numerical examples with four hydro, three

thermal and two wind units are considered for determining the profit at the time period of 24

hours also evaluate the performance of proposed IALO. The simulation results are obtained

from the proposed method in terms of water discharge ware storage volume, hydro power,

thermal power, wind power; reserve power, revenue, total operating cost and Profit

GENCOs are tabulated. Finally, the simulation results are compared with existing

approaches and prove the performance of this proposed algorithm.

Keywords — Optimal Generation Scheduling, Valve point loading effect, Hydro, thermal and

wind generation, Fuel cost minimization, profit maximization, Improved Ant line optimizer.

1. INTRODUCTION

The restructuring of electric power systems has resulted in market-based competition

by creating an open market environment. A restructured system allows the power supply to

function competitively, as well as allowing consumers to choose suppliers of electric energy.

According to this change, traditional methods for power generation operation and control

need modification [1]. Generation scheduling is one of those methods that need changes. On

the other hand, generation scheduling under deregulated environment is more complex and

more competitive than traditional one. Generation companies (GENCOs) run optimal

scheduling not for minimizing total production cost as before but for maximizing their own

GEDRAG & ORGANISATIE REVIEW - ISSN:0921-5077

VOLUME 33 : ISSUE 02 - 2020

http://lemma-tijdschriften.nl/

Page No:942

mailto:[email protected]

mailto:[email protected]

profit. Moreover in the past, utilities had an obligation to serve their customers. That means

all demand and spinning reserve must be met. However, it is not necessary in the restructured

system. The GENCO can now consider a schedule that produces less than the predicted load

demand and reserve but creates a maximum profit [2]

Under deregulated environment, many researchers have proposed various multi-

objective procedures to solve the short-term hydrothermal self-scheduling problem. Mixed

Integer Programming (MIP) based hydro-thermal self-scheduling problem has been described

in a day-ahead joint energy and reserve market [3]. The problem has modeled in the form of

multi-objective framework to simultaneously maximize GENCOs profit and minimize

emissions of thermal units. In the proposed model the valve loading effects which is a

nonlinear function by itself is linearized. Smajo Bisanovic et.al [4] addresses the self-

scheduling problem of determining the UC status for power generation companies before

submitting the hourly bids in a day-ahead market. The hydrothermal model is formulated as a

deterministic optimization problem where expected profit is maximized using the 0/1 mixed-

integer linear programming technique.

A stochastic midterm risk-constrained hydrothermal scheduling problem has been

solved using combined approach of mixed integer programming with Monte Carlo simulation

[5]. The objective of a GENCO is to maximize payoffs and minimize financial risks when

scheduling its midterm generation of thermal, cascaded hydro, and pumped-storage units. The

proposed GENCO solution may be used to schedule midterm fuel and natural water inflow

resources for a few months to a year. The multi-objective function of maximizing the profit

and minimizing the emission of a Hydro -Thermal System (HTS) using Lagrangian

Relaxation-Evolutionary Programming (LR-EP) technique has been presented in the article

[6]. The various constraints of the hydro and thermal units were considered such as power

balance, reservoir storage, turbine flow rate and loading limits of both thermal and hydro

plants. In [7-9], emissions of thermal units are considered as a constraint of objective function

and the valve loading effects and dynamic ramp rat

Wind power generation is continuously increasing around the world, but due to

uncertainty in wind power generation, the unit commitment problem has become complex. A

scenario generation and reduction techniques have been used to consider wind power

uncertainty on system operation by Shukla and Singh [10]. This paper wind-hydro-thermal

coordination problem along with the pumped storage plant was established. Combination of

weighted-improved crazy particle swarm optimization along with a pseudo code based

algorithm and scenario analysis method has been utilized to solve the problem. The

effectiveness and feasibility of this method was tested on systems with and without pumped

storage plant integration.

Siahkali and Vakilian [11] has been proposed a type-2 fuzzy membership function

(MF) has been implemented to model the linguistic uncertainty of type-1 MF of available

wind power generation which stems from opinions of different experts. This approach was

applied to two test systems (six and twenty-six conventional generating units both with two




Page No:943

wind farms) and the results of generation scheduling using both fuzzy modelling type-1, and

type-2 are presented. Lakshmi and Vasantharathna [12] has been proposed an Artificial

Immune System approach for solving generation scheduling problem of a GENCO comprised

of thermal and wind energy systems. In this work, the impact of wind energy on short term

generation scheduling problem is analyzed through the adaptive search which is inspired

from the Artificial Immune System.

Xu et al. [13] has been proposed carbon emission reduction and reliable electricity

generation, an equilibrium strategy based on a hydro-wind-thermal complementary system

under an uncertain environment that fully considers the cooperation of hydro power plants,

wind power plants, and coal combusted thermal power plants. The authors considering the

randomness of seasonal wind speeds, the water flow uncertainty and the fuzziness of coal

thermal plant carbon emissions, the complementary model is more scientific and practical

than current models.

Security constrained generation scheduling (SCGS) problem for a grid incorporating

thermal, wind and photovoltaic (PV) units has been formulated by ElDesouky [14]. The

formulation takes into account the stochastic nature of both wind and PV power output and

imbalance charges due to mismatch between the actual and scheduled wind and PV power

outputs. A genetic algorithm (GA) with artificial neural network (ANN) and a priority list

(PL) was used to minimize the total operating costs while satisfying all operational

constraints considering both conventional and renewable energy generators. Numerical

results are reported and discussed based on the simulation performed on the IEEE 24-bus

reliability test system.

Angarita et al [15] has been proposed a technique that maximizes the joint proft of

hydro and wind generators in a pool-based electricity market, taking into account the

uncertainty of wind power prediction. This imbalance produces overcast in the system, which

must be paid by those who produce it, e.g., wind generators among others. As a result, wind

farm revenue decreases, but it could increase by allowing wind farms to submit their bids to

the markets together with a hydro generating unit, which may easily modify its production

according to the expected imbalance. Dawn and Tiwar [16] developed a approach to optimally

allocate the Thyristor Controlled Series Compensator (TCSC) and Unified Power Flow

Controller (UPFC) with wind generator under deregulated power system..The double auction

bidding model has been incorporated in this paper. The impacts on the locational marginal

pricing and system voltage have been also investigated in this work. The effectiveness of the

proposed approach for optimal placement of TCSC and UPFC has been tested and analyzed

on muddied IEEE 14-bus and muddied IEEE 118-bus systems.

In this paper, addresses the problem of establishing a conceptual frame work using a

new intelligent tool of improved ALO algorithm for wind, thermal and hydro integrated

generation scheduling problem to maximize the profit of GENCOs in the day-ahead energy

and reserve markets. Numerical example with 4 hydro, 3 thermal and 2 wind units with 24

hour test are conceded to illustrate the performance of proposed IALO algorithm.




Page No:944

2. SOLUTION METHODOLOGY

2.1 Overview of Ant Line Optimizer (ALO) algorithm

The ant line optimizer is a meta-heuristic population based search optimization

algorithm. This algorithm recently developed by Seyedali Mirjalili [17] in 2014 and used to

solve the several Engineering constrained and Non-constrained optimizations problems. The

ALO is a trouble-free control parameters algorithm and has colony size, maximum cycle

number and less parameter to tune and getting the global optimal solution. It is inspired by

life cycle of Antlions (doodlebugs), which belong to the Myrmeleontidae family and

Neuroptera order (net-winged insects). The mathematical function and characteristics of ALO

is taken from reference [18].

2.2 Improved ALO

In the ALO algorithm, the ants’ position updates depend on the random walks around

the antlion selected by Roulette wheel and the elite, and the best particle is preserved by

setting the elite in the searching process. These make ALO have the advantages of fast

calculating speed, high efficiency, and good convergence. But, there are phenomenon of the

premature convergence and local optimum for complex optimization problems. Some

improvements are added to enhance optimization ability and accuracy in this section [19-20].

2.2.1. Combination with Particle Swarm Optimization

PSO is a stochastic algorithm that is based on group collaboration by simulating the

behaviour of birds foraging. As described above, the antlion group is one of crucial parts in

the ALO algorithm. So, in this paper, after searching space by ALO, PSO is introduced to

optimize and update the current positions of antlions group in each iteration. Through this

mechanism, the proposed algorithm has characteristics of both ALO and PSO. The antlions

with the ability of communication and memory can move toward the optimal solution faster.

In the search strategy of the newly algorithm, the search characteristics of ALO is kept and

the communication characteristics of PSO is embedded. This can enhance the search

capabilities and improve the searching efficiency in the search period. The searching

strategies of PSO are expressed as [1]

kg

i

kg

i

kg

i

kg

i

kg

i

kg

i xBestSrcxprcvv

2211

1 (1)

11 kg

i

kg

i

kg

i vxx (2)

Where vi is the speed of the ith particle, xi is the position of the ith particle, pi is the best

previous position of the ith particle, Best S is the best previous position among all the

particles, kg is the current iteration, ω is the inertia weight, r1 and r2 are two random variables

in the range [0,1], c1 and c2 are positive constants.

2.2.2. Chaotic Mutation Operator

The mutation operator plays an important role in improving the performance of global

searching. It can accelerate the convergence to the optimal solution and maintain the various




Page No:945

solutions. In this section, a chaotic mutation operator, namely Logistic map, is incorporated

into the improved algorithm and the elite’s position is chosen to be modified by the chaotic

mutation. The mathematical function can be written as:

NNN XXX 11 40 (3)

where N is the current iteration number, λ is a constant.

For different λ, the system of equation (3) takes on different characteristics. It is not

chaotic when 0 < λ < 3. It starts to cycle when λ > 3, and it becomes chaotic status when λ

=4. In this paper, λ is set as 4.

2.2.3. A Serial-Parallel Combined Method to Obtain Mutant Particles

In general, N new particles can be obtained after N mutations of each

element in the elite. This commonly used method to get new particles in this case is

named parallel method. In this paper, a serial-parallel combined method is

proposed. The serial approach is to get the new particles by replacing the

corresponding element in the elite with the new mutates element. This new

approach ensures stochastic character and increases the diversity of the mutant particles

with the same mutation iterations. The procedure is as follows:

(1)Set the elite x0 = (x0 (1),.....,x0(d),....,x0(dim)), dim is the dimension of the elite, Nm is the

iteration number of chaotic mutation.

(2) Loop A: k = 1: Nm

Loop B: d = 1: dim

Convert the position of the elite into a chaos vector y0 in the domain [0,1];

dlbdub

dlbdxdy

0

0 (4)

Where ub(d) and lb(d) are, respectively, upper limit and lower limit in the dth dimension.

Get a new element by Logistic map as follows:

dydydy kkk 11 14 (5)

Where k is the kth iteration, λ is set as 4.

Convert yk(d) into the actual position as follows:

dlbdubdydlbdx kk (6)

Replace x0(d) with xk(d). Obtain the new particle xnew=(x0 (1),.....,x0(d),....,x0(dim)) and

calculate its fitness. If xnew is better, replace x0 with xnew.

End Loop B.




Page No:946

Obtain the new particle xk=(xk (1),.....,xk(d),....,x0(dim)) and calculate the fitness. If is

better, replace x0 with xk Through chaotic mutation and the series-parallel combined method

to obtain mutant particles, there is greater possibility to make the elite to overstep the local

optimum and get a better solution for the new algorithm.

According to the above improvements to the ant lion optimization (ALO), IALO is

summarized below. Figure 2 shows the flowchart of the newly IALO algorithm. In the

following sections, IALO will be applied to identify the parameters of HTGS and the

identification experiments will be used to demonstrate the validity and feasibility of IALO.

3. PROBLEM FORMULATION

3.1 Objective Function

The main objectives of wind integrates hydrothermal scheduling problem under

competitive energy and reserve market is to maximize the total profit of GENCOs. In this

model, in order to meet the market need, power generation performed with the combination

of wind power units and thermal power units. The profit function is the difference between

total revenue and total operating cost of Hydrothermal-wind units. The objective functions

are mathematically defined as

),,,(cos),,,(Re),,,(Pr tkjitTotaltkjivenuetkjiofit (7)

Maximize TCRVPF (8)

The revenue is obtained by sale of wind, hydro and thermal power in the joint energy and

reserve market.

T

t

N

k

WG

T

t

N

j

HG

T

t

N

i

T

t

N

i

TGRTG

WGHG

TG TG

tkVtSPtkPtjXtSPtjP

tiUtRPtiPtiUtSPtiPTR

1 11 1

1 1 1 1

,.,,.,

,.,,.,

(9)

The total operating cost includes power and reserve generation of thermal units, start-up and

shut-down cost of thermal units, operating cost and fixed cost of wind generating units.

T

t

N

i

TGTGTGTG

TG

tiUtiSDtiSUtiRPtiPFTC1 1

,,,,,

T

t

N

k

WG

WG

tkVkFCWGkOCWGtkP1 1

,.,

(10)

Mathematical model of Thermal plant

The total operation expense of a system is the fuel cost of thermal plants. The valve-point

effects, which make the fuel cost function a non-convex curve, are taken into consideration.

The objective function to minimize the fuel cost of thermal plants during the scheduling

horizon can be defined by




Page No:947

tiPtiPieidictiPibtiPiatiPF TGTGTGTGTG ,,sin,,, min2 (11)

Mathematical model of hydro plant

The hydropower generation is a function of water discharge rate and reservoir storage

volume, which can be expressed as follows

jCjQCjVjCjQjVjCjQjCjVjCP HGHGHGHGHGHGHG 6543

2

2

2

1 (12)

3.2 System Constraints

a. Power balance constraints

The sum of power generation committed thermal units and sum of power generation of wind

turbine generators are envisages to be lesser than or equal to the system load demand. Hence,

the eqn. (6.6) becomes

WGHGTG N

k

DWG

N

j

HG

N

i

TG tPtkVtkPtjXtjPtiUtiP111

,.,,.,,.,

(13)

b. Spinning reserve constraints

The sum of the reserve power of committed thermal units during the planning period augurs

to be less than or equal to total spinning reserve of the power plants and is mathematically

defined as in equation (6)

tSRtiUtiPTGN

i

TG

,.,1 (14)

tiPtiPtiR TGTGTG ,,,0 minmax (15)

tiPtiPtiR TGTGTG ,,, max (16)

3.3 Thermal Generator Constraints

c. Thermal unit generation limits

Each thermal generator generate the power of min

TGP to max

TGP and given in eqn. (26)

tiUtiPtiPtiUtiP TGTGTG ,.,,,., maxmin (17)

d. Thermal unit up/down spinning reserve contribution constraints

The thermal unit up/down spinning reserve contribution constraints are shown in eqn. (27) to

(30).




Page No:948

tiPriPiUStiUS TG ,,,min, maxmax (18)

riPtiPiDStiDS TG ,,,min, minmax (19)

Where

riPdiUS ,% maxmax (20)

riPdiDS ,% minmax (21)

e. Thermal unit minimum up/down time constraints

The thermal unit minimum up/down time constraints is mathematically described by eqn.

(31) and eqn. (32).

0,1,1, tiUtiUiMUtitON (22)

01,,1, tiUtiUiMUtitOFF (23)

f. Thermal unit ramp up/down capacity constraints

The thermal unit ramp up/down capacity constraints are written using eqn. (33) and eqn. (34).

tiPriPiURtiUR TG ,,,min, maxmax (24)

tiPriPiDRtiDR TG ,,,min, minmax (25)

3.4 Hydro Generator Constraints

g. Water discharge constraints

The water discharge rate of turbine must be within the maximum and minimum operating

limits given by jQHG

min and jQHG

max espectively

jQtjQjQ HGHGHG

maxmin , (26)

h. Storage volume constraints

The operating volume of the reservoir storage must lie in between the maximum and

minimum capacity limits given by jVHG

min and jVHG

max respectively.

jVtjVjV HGHGHG

maxmin , (27)

3.5 Wind Generator Constraints

i. Wind power curve constraints.

The wind power generation of Kth units as follows




Page No:949

kOvtvkRvkP

kRvtvkIvtvk

kOvtorvkIvtv

tkP

WG

WG

,,,

,,,,

,,,0

,

max

(28)

Where

2max, tCvtBvAjPtvj WG and A, B, C are the constants (29)

j. Total available wind power generation

The total available power is equal to sum of power generation of wind units and it

represented in eqn. (39).

WGN

j

WGWGT tjPtP1

* ,

(30)

k. Total actual wind power generation limit

Wind power generated between zero to actual wind power is written in using eqn. (40).

tPtP WGTWGT

0 (31)

l. Wind power generation fluctuation constraints

The fluctuation of wind power is mathematically represented by eqn. (41) and eqn.(42).

tPtifPtSDRtPtP WGTWGTWGTWGT 1,1 (32)

tPtifPtSURtPtP WGTWGTWGTWGT 1,1 (33)

4. EXECUTION OF IMPROVED ALO ALGORITHM FOR OPTIMAL

GENERATION SCHEDULING OF GENCOs

The technical steps of the proposed algorithm are as follows

4.1 Evaluation and selection of hydro, thermal and wind Variables

Step 1: Read the system data (Forecasted load and reserve demand, market price) and

generator data of hydro, thermal and wind test system..

Step 2: Initialize the proposed IALO algorithmic parameters such as population size NP,

maximum number of generation G, probability of the crossover rate CR and mutation rate

MR.

Step 3: Randomly initialize the population of all dependent variables like water discharge

rate, thermal plant generation outputs and velocity of the wind units.

maxmin, QjQjrandtjQHG (34)




Page No:950

maxmin, PiPirandtiPTG (35)

maxmin, VkVkrandtkVWG (36)

Step 4: Determine water discharge rate for the last interval of time while satisfying the initial

and final reservoir constraints using the following equation.

iRu

k

T

j

HG

T

j

HG

T

j

HG

end

HG

begin

HGHG ikTdjkQtjItjQjVjVtjQ1 11

1

1

,,,,, (37)

Step 5: Check the water discharge for its minimum and maximum limits. If it is less than the

minimum limits it is made equal to its minimum value and if it is greater than maximum limit

it is made equal to maximum limit.

Step 6: Compute the reservoir water storage volume of jth hydro plant for tth time interval

using equation.

T

t

Rui

I

T

j

HGHGHGHG tjIjttIQTjVjV1 1 1

,1,0, (38)

Step 7: Check for the operating limits of water storage volume.

jVtjV HGHG

min, if jVtjV HGHG

min, (39)

jVtjV HGHG

max, if jVtjV HGHG

max, (40)

Step 8: Estimate the hydro power generation of jth hydro plant for tth time interval using

equation (21).

Step 9: Check it for its minimum and maximum limits.

jPtjP HGHG

min, if jPtjP HGHG

min, (41)

jPtjP HGHG

max, if jPtjP HGHG

max, (42)

Step 10: Compute the hydro wind power generation of kth hydro plant for tth time interval

using equation (51)

kOvtvkRvkP

kRvtvkIvtvk

kOvtorvkIvtv

tkP

WG

WG

,,,

,,,,

,,,0

,

max

(43)




Page No:951

Step 11: The thermal and wind generation of plants can be estimated using equation (2i) and

(51) by subtracting hydro generation from the power demand by neglecting transmission

losses.

0,,,111

WGHGTG N

k

DWG

N

j

HG

N

i

TG tPtkPtjPtiP (44)

Step 12: Check the inequality constraints of thermal power, if it is less than minimum limits it

is made equal to its minimum value and if it is greater than maximum limit it is made equal to

maximum limit.

4.2 Implementation of IALO algorithm

Step 13: Initialization. Randomly initialize the positions of ants and antlions.

T

WGNWGkWGWG

HGNHGjHGHGTGNTGiTGTG

WG

HGTG

VVVV

QQQQPPPP

,....,,.....,,

,,....,,.....,,,,....,,.....,,

21

2121 (45)

Where

TGiTTGitTGiTGiTGi PPPPP ...,,...,, 211 (46)

HGjTHGjtHGjHGjHGj QQQQQ ...,,...,, 211 (47)

WGkTWGktWGkWGkWGk VVVVV ...,,...,, 211

Step 14: Calculate the fitness of the antlions and choose the antlion whose fitness is best as

the elite.

Step 15: Select an antlion using Roulette wheel and calculate the random walks around the

chosen antlion and the elite. Update the ants’ position..

Step 16: Repeat Step 3 until the positions of all the ants are updated.

Step 17: Update the antlions’ positions with Equation (1). Compare fitnesses of the new

antlions with the fitness of the elite. If the antlion has better fitness than the elite, then the

elite will be replaced by the position of the antlion.

Step 18: PSO is adopted to search better antlions with Equations (1) and (2). Update the elite.

Step 19: Chaotic mutation is conducted for the elite and gets the mutant particles using a

serial-parallel combined method with Equations (4)–(6).

Step 20: Repeat Step 14 to Step 18 until the stop criteria are met.




Page No:952

5. RESULTS AND DISCUSSION

In order to prove the performance and efficiency of the proposed IALO algorithm, it

has been applied on a test system to solve generation scheduling problem for maximizing the

GENCOs profit under deregulated environment. The proposed test system consists of hydro,

wind and thermal units with valve point loading effect. The proposed algorithm is

programmed in MATLAB 14.0 and numerical simulations are carried out in a computer with

i3 processor, Intel (R), core (i3), is 2.40 GHz, 4GB RAM.

In this assignment, a test system has been considered, to illustrate the proposed

ITLBO based wind integrated hydrothermal scheduling problem. The data for valve point

loading effect of thermal units are adopted from the reference [21]. The proposed test system

consists of a multi-chain cascade of four hydro plants, two wind and three thermal units

In order to maximize the profit of GENCOs, the wind, hydro and thermal system need

proper scheduling that must satisfy constraints such as Power balance, Generator limits of

wind, hydro and thermal units, water storage and discharge limits of hydro units and wind

power curve constraints. So it is recommended that the improved ALO can directly solve to

solve the optimal scheduling problem considering the valve-point loading effect of thermal

units.

The characteristic of the hydro power plant is described by considering the reservoir

storage limits, plant discharge limits, generation limits and the initial and final station of

reservoir. The corresponding data is taken from same reference [21] and it is provide power

generation coefficients of hydro generation units and thermal plants. Hour-by-hour forecasted

load demand, Reserve demand and market price of power system is taken from reference [12].

This problem is analyzed in two different cases to maximize the [profit of GENCOs such as

Case - 1:Wind integrated Hydrothermal generation scheduling without reserve power

generation

Case - 2: Spinning reserve constrained Wind integrated Hydrothermal generation

scheduling.

Case- 1

In the first case, load demand and fore casted market price only used to determine

profit of GENCOs by the optimal schedule of the thermal, hydro and wind turbine units. The

maximum power demand of 1150 MW is predicted for the test system at 12th hour in the

scheduled time period. Here, the wind, Hydro and thermal units dispatch power is lesser than

or equal to the forecasted load demand.

The powerful searching operators of the IALO effectively optimize the system

variables of water discharge, water storage volume, wind speed and real power of thermal

units with help of PSO algorithm. A chaotic mutation operation is applied for the elite to

break out of the local optimum and obtain the global optimal solutions. The optimized

parameters of best water discharge and storage volume for 24 hour time period is presented in




Page No:953

Table 1. The hydro power generation is obtained by the optimized value of water discharge

and storage volume of four hydro plants. The optimal generation scheduling of four hydro

power generations, two wind power units and three thermal power generations is shown in

Table 2. In this paper, unit commitment process is done for thermal units. From table 6, the

thermal unit 1 should be de-committed for entire planning period because of its high start-up

cost.

Table 1 Water discharge and water storage volume of proposed test system

Hour

(h)

Water Discharge (∗ 𝟏𝟎𝟒𝒎𝟑) Volume (∗ 𝟏𝟎𝟒𝒎𝟑)

Plant1 Plant2 Plant3 Plant4 Plant1 Plant2 Plant3 Plant4

1 15.5000 15.3760 30.4970 22.6540 95.0000 73.1240 148.1030 100.6460

2 15.8790 15.4950 30.4980 24.0530 89.5000 65.7480 125.7060 80.7920

3 15.5000 15.4500 30.4990 25.5000 83.0210 60.0000 113.0080 70.0000

4 15.4580 15.4710 30.4960 25.4970 80.0000 60.0000 102.4090 70.0000

5 12.3750 15.8390 30.9000 13.9290 80.0000 60.0000 104.7680 70.0000

6 13.1310 15.2780 21.8380 13.3290 80.0000 60.0000 107.8630 86.5680

7 15.8970 15.9000 20.1290 13.3040 80.0000 60.0000 120.9330 103.7370

8 15.4880 15.4650 22.5270 14.6130 80.0000 60.0000 131.6500 120.3320

9 8.1780 15.4990 19.4620 15.9770 80.0000 60.0000 140.0930 136.2150

10 14.9380 15.4750 19.2320 17.1570 81.8220 60.0000 152.8060 151.1380

11 15.8020 15.6130 20.8740 19.1690 80.0000 60.0000 165.9620 155.8190

12 15.4730 15.5000 21.9000 19.7380 80.0000 60.0000 169.7310 156.7790

13 12.6040 15.2310 20.8750 19.3900 80.0000 60.0000 180.2680 159.5680

14 15.0000 15.4060 20.2710 19.9650 80.0000 60.0000 194.6700 159.6400

15 15.3170 15.6870 24.0970 19.7760 80.0000 60.0000 208.4850 158.9070

16 15.3940 15.4560 19.9860 22.9850 80.0000 60.0000 215.4920 160.0000

17 15.4990 15.2540 20.6010 19.9940 80.0000 60.0000 227.7370 158.9150

18 14.6080 15.0750 19.7230 20.2760 80.0000 60.0000 239.8590 159.7960

19 14.2530 15.2850 18.3660 23.7090 80.0000 60.0000 240.0000 159.7910

20 15.1730 13.8460 16.9250 21.2320 80.0000 60.0000 240.0000 160.0000

21 14.8630 15.3000 16.1610 18.9020 80.0000 60.0000 240.0000 158.7540

22 15.3000 15.2920 30.3000 24.1530 80.0000 60.0000 240.0000 160.0000

23 15.8910 12.3040 15.7160 24.4450 80.0000 60.0000 240.0000 155.5700

24 5.9000 6.9000 16.2010 25.9000 80.0000 60.0000 240.0000 149.4910




Page No:954

Table 2 Hydro, wind and thermal power generation of proposed test system without

reserve power generation

Hour

(h)

Hydro power

(MW)

Wind power

(MW)

Thermal power

(MW)

Ph1 Ph2 Ph3 Ph1 Pw2 PW3 Ps1 Ps2 Ps3

1 95.8650 83.9838 0.0000 244.1652 41.5693 37.7039 0.0000 0.0000 246.7128

2 92.6263 78.1170 0.0000 216.6198 44.729 37.7039 0.0000 0.0000 310.2102

3 88.4702 73.0693 0.0000 199.7175 46.2842 37.7039 0.0000 0.0000 254.7550

4 86.4403 73.0928 0.0000 199.7173 47.8286 36.0062 0.0000 0.0000 206.9148

5 84.2509 73.4634 0.0000 157.2865 49.3511 29.5781 0.0000 0.0000 276.0699

6 85.5267 72.8660 10.7263 174.8609 47.8286 29.5781 0.0000 0.0000 378.6135

7 86.1027 73.5170 26.3496 200.7673 41.5693 29.5781 0.0000 251.2702 240.8457

8 86.4224 73.0861 17.8550 225.7005 41.5693 37.7039 0.0000 272.5976 255.0651

9 68.4377 73.1239 37.2305 253.7923 44.7229 46.4599 0.0000 295.7415 270.4913

10 87.8488 73.0973 42.6416 278.0692 49.3511 55.1571 0.0000 252. 242 241.5400

11 86.1895 73.2455 39.7996 296.6432 56.4639 55.1571 0.0000 251.4905 241.0108

12 86.4314 73.1250 35.8648 301.1339 56.4639 69.6196 0.0000 272.4274 254.9340

13 84.6881 72.8074 43.9191 301.8394 62.2912 69.6196 0.0000 240.9046 233.9307

14 86.6200 73.0189 49.8969 305.4252 62.2912 69.6196 0.0000 0.0000 383.1282

15 86.5144 73.3202 33.7891 303.5465 62.2912 69.6196 0.0000 0.0000 380.9189

16 86.4760 73.0760 54.6082 320.9090 62.2912 69.6196 0.0000 0.0000 393.0200

17 86.4156 72.8362 53.9404 304.8544 56.4639 55.1571 0.0000 208. 253 212.1270

18 86.6339 72.6033 57.8785 307.4006 56.4639 46.4599 0.0000 251.5351 241.0249

19 86.5350 72.8746 61.3698 323.4585 49.3551 46.4599 0.0000 213.9681 215.98300

20 86.5728 70.4849 63.8588 312.8229 49.3551 37.7039 0.0000 213.5304 215.6752

21 86.6395 72.8930 64.6731 297.8875 41.5693 37.7039 0.0000 0.0000 308.6337

22 86.522 72.8832 0.0000 325.2391 41.5693 36.0062 0.0000 0.0000 297.7799

23 86.1084 66.5451 64.9860 321.0803 41.5693 34.3393 0.0000 0.0000 235.3716

24 53.6598 41.4770 64.6391 317.4123 41.5693 36.0062 0.0000 0.0000 245.2362

Table 3 Simulation results of proposed test systems without reserve power generation

Hour

(h)

Load Demand

(MW)

Revenue

($)

Thermal cost

($)

Wind cost

($)

Profit

($)

1 750 16612.50 759.3980 641.6790 15211.40

2 780 17160.00 945.7070 665.3300 15548.90

3 700 16170.00 782.3360 677.0400 14710.60

4 650 14722.50 648.7420 673.7690 13400.00

5 670 15577.50 844.0690 628.9410 14104.50

6 800 18360.00 1160.1100 617.5220 16582.40

7 950 21375.00 1508.8700 570.5780 19295.60

8 1010 22371.50 1609.9600 641.6790 20119.90

9 1090 24852.00 1721.3600 741.9450 22388.70

10 1080 31698.00 1513.7200 852.7580 29331.50

11 1100 33165.00 1509.9600 906.1040 30748.90

12 1150 36397.50 1609.1000 1032.6500 33755.80

13 1110 27306.00 1460.2700 1076.3600 24769.40




Page No:955

14 1030 25235.00 1174.7500 1076.3600 22983.90

15 1010 22725.00 1167.5800 1076.3600 20481.10

16 1060 23638.00 1207.0400 1076.3600 21354.16

17 1050 23362.50 1309.3500 906.1040 21147.00

18 1120 24696.00 1510.1200 830.0030 22355.90

19 1070 23754.00 1335.7300 776.6570 21641.60

20 1050 23782.50 1333.6800 700.0420 21748.80

21 910 21021.00 941.0130 641.6790 19438.30

22 860 19737.00 908.3470 626.8250 18201.80

23 850 19337.50 727.3800 612.2390 17997.90

24 800 18040.00 755.2070 625.8250 16658.00

Total profit ($) 493980.00

Table 3 explains the simulation results of 3 thermal, 4 hydro and 2 wind test system. It

includes power demand, thermal cost, wind cost, total operating cost, revenue and profits of

hydro, thermal and wind generating units for 24 hours time period. The obtained total profit

is $ 493980.00 and computational time is 102 sec.

Case - 2

In the second case, spinning reserve has been included in the objective function. The

revenue obtained from sale of generated power and reserve allocation and the profit of

GENCOs are calculated in both energy and reserve market. The additional spinning reserve

requirement is assumed to be 10% of forecasted load demand and reserve prices are taken as

10% of actual energy prices. The average operation and maintenance cost of a wind turbine

generator is 1.25%of the capital cost. Power generation and reserve allocation of wind

integrated hydrothermal system are presented in Table 4.

Fig.1. Power generation of two wind farm




Page No:956

Fig.2. Power generation of thermal, hydro and wind farm

The IALO operators optimize the hydro, thermal and wind variables also considering

the reserve demand and reserve price of the proposed test system and determine fitness value

of objective function. Also satisfy the standard system and unit constraints of wind, hydro

and thermal units. The graphical representation of power generation of two wind farm is

displayed in fig. 1. The total thermal, hydro and wind power generation for 24 hour time

period are obtained by proposed method and shown in fig. 2.

Table 4 Hydro, wind and thermal power generation of proposed test system considering

reserve power generation

Hour

(h)

Hydro power

(MW)

Wind power

(MW)

Thermal power

(MW)

Reserve power

(MW)

Ph1 Ph2 Ph3 Ph1 Pw1 Pw1 Ps1 Ps2 Ps3 Rs1 Rs2 Rs3

1 95.8650 83.9838 0.0000 244.1652 41.5693 37.7039 0.0000 0.0000 321.7128 0.0000 0.0000 75.0000

2 92.4322 78.5447 0.0000 217.0776 44.7229 37.7039 0.0000 0.0000 387.5189 0.0000 0.0000 77.3087

3 88.2025 73.0693 0.0000 199.7175 46.2842 37.7039 0.0000 0.0000 325.0227 0.0000 0.0000 70.2677

4 86.4403 73.0928 0.0000 199.7173 47.8286 36.0062 0.0000 0.0000 271.9148 0.0000 0.0000 65.0000

5 83.8331 73.2721 0.0000 155.8233 49.3511 29.5781 0.0000 0.0000 345.1422 0.0000 0.0000 69.0723

6 85.5267 72.8660 11.0320 175.1169 47.8286 29.5781 0.0000 0.0000 458.0518 0.0000 0.0000 79.4383

7 86.5236 72.8930 29.4335 196.4524 41.5693 29.5781 0.0000 300.0000 288.5501 0.0000 48.7298 47.7044

8 86,5276 72.8499 19.5174 225.3746 41.5693 37.7039 0.0000 300.0000 327.4574 0.0000 27.4024 72.3923

9 67.3148 72.8918 38.4314 253.6878 44.7229 46.4599 0.0000 300.0000 375.4914 0.0000 4.2585 105.0001

10 87.8787 73.4953 41.2346 282.4012 49.3511 55.1571 0.0000 300.0000 298.4820 0.0000 58.4600 56.9420

11 86.5625 72.5181 42.3299 293.7416 56.4639 55.1571 0.0000 300.0000 303.2269 0.0000 48.5095 62.2161

12 86.1253 73.5170 33.5834 304.5226 56.4639 69.6196 0.0000 300.0000 341.1683 0.0000 27.5726 86.2343

13 85.3459 73.2640 41.9074 304.7107 62.2912 69.6196 0.0000 300.0000 283.8613 0.0000 59.0954 49.9306

14 86.6432 72.7757 50.4204 304.0231 62.2912 69.6196 0.0000 0.0000 487.2269 0.0000 0.0000 104.0987

15 86.5909 73.1106 34.728 302.7338 62.2912 69.6196 0.0000 0.0000 481.9321 0.0000 0.0000 101.0132

16 86.3530 73.2893 53.8726 321.7105 62.2912 69.6196 0.0000 0.0000 498.8638 0.0000 0.0000 105.8438

17 86.5227 72.5747 54.6414 303.8672 56.4639 55.1571 0.0000 271.4656 254.3074 0.0000 59.3386 42.1804

18 86.5602 73.3083 55.9580 310.9480 56.4639 46.4599 0.0000 300.0000 302.3017 0.0000 48.4649 61.2768

19 86.6388 73.3182 60.4579 324.1789 49.3511 46.4599 0.0000 277.9647 258.6304 0.0000 63.9966 42.6474

20 86.5728 70.4849 63.8588 311.7486 49.3511 37.7039 0.0000 277.1608 258.1191 0.0000 63.6304 42.4439

21 86.4374 73.5170 64.0631 600.8857 41.5693 37.7039 0.0000 0.0000 396.8236 0.0000 0.0000 88.1899

22 86.4150 73.1162 0.0000 324.5675 41.5693 36.0062 0.0000 0.0000 384.3257 0.0000 0.0000 86.5458

23 86.1084 66.5451 64.9860 320.1872 41.5693 34.3393 0.0000 0.0000 321.2647 0.0000 0.0000 85.8931

24 50.6150 38.9250 64.9354 316.1227 41.5693 36.0062 0.0000 0.0000 331.8263 0.0000 0.0000 86.5901




Page No:957

Table 5 Simulation results of proposed test system considering reserve power generation

Hour

(h)

Load and

Reserve

Demand (MW)

Revenue

($)

Thermal cost

($)

Wind cost

($)

Profit

($)

1 825 18273.80 980.8460 641.6790 16651.20

2 858 18876.00 1189.0500 665.3300 17021.60

3 770 17787.00 991.0070 677.0400 16119.10

4 715 16194.80 831.9280 673.7690 14689.10

5 737 17135.30 1053.4800 628.9410 15452.80

6 880 20196.00 1426.6300 617.5220 18151.90

7 1045 23512.50 1786.8500 570.5780 21155.10

8 1111 24608.60 1904.5000 641.6790 22062.50

9 1199 27337.20 2056.0200 741.9450 24539.20

10 1188 34867.80 1816.4500 852.7580 32198.60

11 1210 36481.50 1830.7000 906.1040 33744.70

12 1265 40037.30 1947.0500 1032.650 3705.60

13 1221 30036.60 1772.9700 1076.360 27187.30

14 1133 27758.50 1529.2600 1076.360 25152.90

15 1111 24997.50 1510.4500 1076.360 22410.70

16 1166 26001.80 1570.9100 1076.360 23354.50

17 1155 25698.80 1604.5500 906.1040 23188.10

18 1232 27165.60 1827.9100 830.0030 24507.70

19 1177 26129.40 1635.600 776.6570 23717.10

20 1155 26160.80 1631.8200 700.0420 23828.90

21 1001 23123.10 1219.5300 641.6790 21261.90

22 946 21710.70 1178.6400 626.8250 19905.20

23 935 21271.30 979.4720 612.2390 19679.50

24 880 19844.00 1012.0000 626.8250 18205.20

Total profit ($) 541240.00

Table 6 Comparison of fuel cost of proposed with existing methods

Method Best total fuel cost, $

IALO 63963.0000

MPSO [21] 66,083.6629

PSO [21] 68,646.8010

GA [21] 71016.9724

His [21] 71300.9716

JAYA [21] 85394.0271




Page No:958

Fig.3. Comparison of fuel cost of proposed with existing methods

Fig.4. Comparison of profit of with and without reserve power generation

The simulation results of spinning reserve constrained proposed system is reported in

Table 5. This table lists out the revenue, thermal cost, wind cost and profits of GENCOs

under energy and reserve market. The total profit of proposed system is $ 541240.00 and

computational time is 120 sec. The comparative studies are made to prove effectiveness of

proposed method. The total operating cost of proposed with existing methods such as MPSO,

PSO, GA, HSA and JAYA are compared and displayed in Table 6 and graphically

represented in fig. 3. The comparison of profit of with and without reserve power generation

of the test systems are shown in fig. 4. From the results, we come to know that the suggested

algorithm provides maximized profit, minimum fuel cost and less computational burden

when compared with existing literature.




Page No:959

6. CONCLUSION

This article contributes the solution of price based generation scheduling problem to

maximize the profit of GENCOs under competitive environment. This paper has been

integrating the renewable energy source of wind and hydro generating units with thermal

power plants. The problem has been solved considering reserve power generation and valve

point loading effect. The suggested improved ALO is proposed to solve this problem. The

problem is modelled as stochastic optimization problem that is maximize the profit of

GENCOs subjected to standard prevailing wind, hydro and thermal constraints. By

integrating hydro, wind and thermal system, the profit is more when compared with using

thermal generators alone for power generation. Case study with 3 thermal, 4 hydro and 2

wind units with 24 hour time period is considered to validate the performance of applied

Imposed ALO. The simulation results are compared with other evolutionary programming

techniques From the comparisons, this approach is one of the best and reliable approach for

solving of engineering optimization problems.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the authorities of Annamalai University for the

facilities offered to carry out this work.

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BIOGRAPHY OF AUTHORS

T.Anbazhagi (Thirumurugan Anbazhagi) received the B.E degree in

Electrical and Electronics Engineering from Arasu Engineering College in

2009 and the M.E degree in Power Systems from AnnamalaiUniversity,

Annamalai Nagar, India in 2013. She is currently pursuing her research

program in the Department of Electrical Engineering; Annamalai University.

Her areas of interest are analysis of electrical machines, power system

optimization, Optimal generation scheduling, Deregulated power systems, renewable energy

and soft computing techniques.

K. Asokan (Kaliyamoorthy Asokan) received the M.E degree in Power

Systems and the PhD degree in Electrical and Electronics Engineering from

Department of EEE, Annamalai University, Annamalainagar, India in the year

2008 and 2015 respectively. He is currently working as a Assistant Professor in

the same department (on Deputation to Government College of Engineering,

Bargur).. His research interests include power system operation and control, Hydrothermal

Scheduling, Renewable energy Sources, Deregulated power systems and Computational

intelligence applications

R. AshokKumar (Ramaswamy AshokKumar) is presently the Professor of

Electrical Engineering, Annamalai University, India .His research interest

includes Power system operation and control, Design analysis of Electrical

Machines, Radial distributed system and deregulated power system studies. He

has published many reports and journal articles in his research area. He

received M.E degree (Power System Engineering) in 1999 and Ph.D degree in 2009 both

from Annamalai University. In 1994 he joined Annamalai University as a Lecturer then

elevated to the level of Professor. He is a member of ISTE and other technical bodies




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